Experimental Validation of Real Gas CO2 Model near Critical … · 2017-03-30 · Experimental...
Transcript of Experimental Validation of Real Gas CO2 Model near Critical … · 2017-03-30 · Experimental...
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Experimental Validation of Real Gas CO2 Model near
Critical Conditions
1
March 30, 2016
D. Paxson, C. Lettieri*, Z. Spakovszky
MIT Gas Turbine Lab
P. Bryanston-Cross, Univ. of Warwick
A. Nakaniwa
Mitsubishi Heavy Industries
*Currently at TU Delft
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Key Takeaways 2
• First experimental characterization of metastable CO2
• Preliminary CO2 measurements demonstrate applicability of RefProp
implementation of Span and Wagner equation of state in metastable
region
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CO2 Compression for Carbon Capture and Sequestration
• Mitigation of CO2 emissions require compression to high pressure
• Compressor power requirements limits large-scale CCS viability
Imaged Credit: Cal CCS Image Credit Mitsubishi Heavy Industries
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Two-Phase Flow Near Impeller Leading Edge 4
• Acceleration over leading edge leads to localized cooling and
possible condensation1,2
• Rapid rate of cooling causes non-equilibrium phase-change
Condensing
Region
Compressor
Blade P/P0
1.5
0.8
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Non-Equilibrium Condensation 5
A
E
C
Liquid
Gas
Supercritical
Metastable
D
250 350 300
100
50
Temperature [K]
Pre
ssure
[b
ar]
B
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Calculating Metastable State Properties 6
Ideal Gas Approximation
• Used for low density condensing gases1,2 and gas mixtures2
Equation of State (EOS) Extrapolation3
• Current state of the art for metastable steam vapor
• Span and Wagner is state-of-the-art EOS for CO2
• Implemented through Refprop
• Limited to values below EOS spinodal limit
Direct Tabular Extrapolation4
• Simpler than EOS extrapolation
• Invalid for large excursions into two-phase dome
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Equilibrium Pressure-Temperature Diagram 7
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Direct Extrapolation of Metastable Properties 7 8
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Built-in EOS Extrapolation Capability with RefProp 9
Metastable
Region
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Objectives and Goals 10
• Demonstrate the use of interferometery for density measurement in a
metastable vapor
• Fully characterize the thermodynamic state of metastable CO2
• Determine the ranges of applicability for EOS and direct
extrapolation methods
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Experimental Blowdown Rig 11
Liquid CO2 Dewar
Liquid CO2 Pump
Transparent 2-D test section
High Pressure and Temperature Charge Tank Dump Tank
Vacuum Pump
Typical Rig Parameters
Parameter Typical Value
Throat Area [mm2] 50
Tank CO2 Mass [kg] 50-500
Blowdown Time [s] 0.5-2
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Con-Di Nozzle as Surrogate for Impeller Leading Edge
Saturated
Region
Saturated
Region
Condensing
Region
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Absolute Limits on Test-Rig Operating Conditions 13
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Test-Section Requirements 14
• Optical access
• High pressure measurement resolution
• Ability to easily modify nozzle geometry
• Short testing turn-around time
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Test-Section Design 15
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Interferometry for Nozzle Density Measurement 16
Lamanna et. al.5
• Measured density distribution across condensation shocks in low
pressure nitrogen
• Densities on the order of 1kg/m3
Duff4
• Measured densities in condensing CO2 away from the critical point
• Densities on the order of 10kg/m3
Current Research
• Measured densities in condensing CO2 near the critical point
• Densities on the order of 100-1000kg/m3
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Shearing Interferometer 17
4. 50% Beam
Splitter
1. Laser
2. Beam
Expander
3. Collimating
Lens
Test Section
Windows
Interfering
Beams
Direction of
Flow
6. Mirror
5. Mirror
7. Displaced
Beam Splitter
8. C
CD
Cam
era
Nozzle
Density
Gradient
1. 2. 3.
4. 5.
6. 7. 8.
Fixed Beam
Displaced Beam
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Wavefront Distortion through Nozzle Density Gradient
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Nozzle
Density
Gradient
Coherent
Wavefront Distorted
Wavefront
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Fringe Pattern in Shearing Interferometer
19
Carrier Fringe
Pattern
displacement
Without Flow in Nozzle
Phase Stretched
Fringe Pattern
With Flow in Nozzle
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1-D Phase Unwrapping Method 20
Continuous Phase Map
x-location P
ha
se
FFT / IFFT
Phase
Unwrapping
x-location
Pix
el V
alu
e
Raw Image
Discontinuous Phase Map
x-location
Ph
ase
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Post-Processing Procedure 21
Derivative of Fringe Phase Lag
Optical Path Length Difference
Density
Phase Lag
Index of Refraction
Integration
x λ/2π
/T-S Width
Lorentz-
Lorenz
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2-D Phase Unwrapping Method8 22
Raw Image
Discontinuous Phase Map
Continuous Phase Map
Phase
Unwrapping
FFT
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Shearing Interferometer Measures Density Gradient 23
Requirement: Beam displacement measurement accuracy < 5 μm
Inte
rfero
me
ter
Ou
tpu
t
Nozzle Location
Beam
displacement
De
nsity
Nozzle Location
Fixed Beam
Displaced Beam
Integration
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Key Idea: Knife Edge Diffraction Pattern 24
• Perpendicular knife edge produces a repeatable pattern to determine
location
Diffra
ctio
n
Pa
ttern
Knife
Edge
Propagating Beam
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Schematic of Displacement Measurement 25
Knife Edge
Beam Blocker
Beam
Blocker
(Front
View)
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Beam Blocker Setup 26
Beam Blocker
Knife Edge
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Knife Edge Detection 27
Smooth
Edge
location
Curve Fit
~1cm
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Displaced Knife Edge Image 28
Knife Edge
(Both Beams Blocked)
Displaced Image
(Left Beam Blocked)
Fixed Beam
(Right Beam Blocked)
displacement
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Displacement Measurement Accurate to 5μm (~2%)
• Images taken at 4 micrometer settings to compare multiple points
• Knife edge measurement method yields sub pixel accuracy with error below 5
microns (order of magnitude improvement over traditional method)
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Micrometer
Setting [μm]
Calculated
Displacement [μm] Error [μm]
0 0 0
50 47.12 2.88
100 103.26 3.26
150 154.36 4.36
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Mach Waves Limit Observation to Subsonic Section
• Density gradients make it difficult to determine fringe pattern and
density in downstream section
• Improvements in nozzle surface finish and diverging angle will be
investigated to improve performance
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Mapping Compressor Mach Number to Nozzle 31
• Measurements in nozzle limited to Mach number of 1
• Typical maximum Mach numbers at impeller leading edge: 1.1-1.2
• Nozzle total conditions reduced to drive throat conditions farther into
metastable region.
• Compressor Mach numbers mapped onto experimental capability to
characterize metastable behavior in region of interest
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Range of Metastable Region Covered 32
Sonic Line - Nozzle
Sonic Line - Compressor
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First Experimental Blowdown Runs 33
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Metastable Density Comparison: Expansion A
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Metastable Density Comparison: Expansion B
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Blowdown Run Comparison: Reduced Quantities
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Conclusions and Future Work
Conclusions
• First interferometry measurements in S-CO2 to fully characterize
metastable state
• RefProp metastable properties accurate to within 3%
• Direct (tabular) extrapolation of metastable properties accurate to
within 7%
Future Work
• Quantify error in density measurement at varying total conditions
• Determine under which conditions direct extrapolation is valid for
determination of metastable properties
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Acknowledgment
This research was funded by Mitsubishi Heavy Industries Takasago
R&D Center, which is gratefully acknowledged. In particular, the
authors would like to thank Dr. Eisaku Ito, and Mr.Akihiro Nakaniwa for
their support.
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